A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation

Charles Bouman, Purdue University, School of Electrical Engineering
Ken Sauer, University of Notre Dame, Department of Electrical Engineering

Document Type Article


We present a Markov random field model intended to allow realistic edges in maximum a posteriori ( M A P ) image estimates, while providing stable solutions. Similar to the generalized Gaussian distribution used in robust detection and estimation, we proposed the generalized Gaussian Markov random field (GGMRF). This model satisfies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique local minimum of the a posteriori log likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low dosage transmission tomography.